A recursive function is a function in code that refers to itself for execution.

## Recursion vs. Looping in Python

Recursive functions can be simple or elaborate. They allow for more efficient code writing, for instance, in the listing or compiling of sets of numbers, strings or other variables through a single reiterated process.

Recursive functions in code often rely on loop setups, where the initial variable is called on multiple times while being altered by the loop.

Simple examples of a recursive function include the factorial, where an integer is multiplied by itself while being incrementally lowered. In addition to simpler recursive functions, programmers and others have come up with much more elaborate functions that also work through principles of recursion.

Some, like the Fibonacci sequence, have applications to finance and other areas, where others remain esoteric and largely exclusive to the IT community.

Toggle navigation Menu. Recursive Function Last Updated: June 13, Definition - What does Recursive Function mean? Techopedia explains Recursive Function Recursive functions in code often rely on loop setups, where the initial variable is called on multiple times while being altered by the loop.

Share this:. Related Terms. Related Articles. Machine Learning: 4 Business Adoption Roadblocks. What is the difference between little endian and big endian data formats? What circumstances led to the rise of the big data ecosystem?

What considerations are most important when deciding which big data solutions to implement? More of your questions answered by our Experts. Related Tags. Development Programming Tools Computer Science. Machine Learning and Why It Matters:. Latest Articles.One of the most fundamental tools in programming is a loop. While there are many different types of loops, almost each type of loop has the same basic function: iterating over data to analyze or manipulate it. Recursion is another popular type of function and although it can also analyze and manipulate sequences of data similar to a loop, recursion is probably less understood in many cases, and can often be somewhat confusing.

Almost all recursive functions can be re-written as loops, and vice versa. A for loop is used for iterating over a sequence that is either a list, a tuple, a dictionary, a set, or a string. A for loop terminates whenever it reaches the end of the sequence of data. But if we turn it into a function, it allows us to reuse the same function to add numbers below 10, or 20, or whatever.

There could be cases where we would need two values to be added, without knowing what the values were, so having a function that would return the sum of numbers below a certain value could be handy.

Opgi g bodyIn order to make this loop work, we would need to have all of the numbers stored as a list so that we could iterate over each element and add it to the total. Our function starts by taking in a number as a parameter. If we run this code, we can see that at each iteration, we have the number we expect, and we are returned the total. Recursion occurs when any function calls itself.

D3 tree v5One of the big differences between recursion and looping is the way that a recursive function terminates. In the above example, a for loop ends at the end of the sequence it is looping over. Instead, recursive functions have what is called a base condition.

Malavika raghunathan mdA base condition is one that will terminate the loop if the condition is met. At each function the the function either calls itself with new inputs, or returns a value.

Here, we can pass in a starting number, and a total variable. When the function is first called, the total is 0 and the number is 5. We check to see if the number is 0.One of the applications I work on exposes flattened reporting data as a SQL view. The systems that consume this data only support fetching it via direct database access, so I had to implement it as a read only view. The view itself is fairly complex, combining relational and summary data from 15 different tables.

The most challenging aspect of writing this was working with a hierarchical, self-referential table. Each row of reporting data in the view belonged to a node in this hierarchy, and the view itself needed to include data from the associated root node. To make this a little more concrete, imagine you had an arbitrarily deep nested category tree with products in each category.

Since the category hierarchy can be arbitrarily deep, no fixed set of SQL query or join operations can solve what is a recursive problem. You need looping or recursion to find your way to the root category. This is not strictly true if you are willing to accept some de-normalization of the self-referential tables.

I will discuss one of these techniques and its limitations next. Working with hierarchical data in SQL can be hard. In the end these all required adding moving parts to the system just to support one reporting view.

Error fddn580 pes 2019They add powerful recursion capabilities to the SQL toolkit and are well supported by most relational databases. As applied to my problem they performed exactly the recursion I needed and added no additional moving parts. The downside to this is the data de-normalization, we are duplicating data implicit in the hierarchy into an explicit column.

Untaken ubisoft namesThere are also forms that include efficient category sibling ordering for free. If possible I wanted to avoid adding all of these moving parts just to support one reporting view.

In its non-recursive usage a CTE behaves like a named sub-select.

## Recursion and stack

The syntax looks like this:. Far more interesting and powerful is the recursive CTE. This continues recursively so the second SELECT is run against all the rows from the last iteration and the new rows are added to the result set.

Recursive CTEs are supported by all the major relational databases. Here is some sample data in CSV format for the remaining examples. This defines a simple hierarchy with two root categories, each with its own sub-tree of categories. The first example will let us query all of the categories in the sub-tree staring with the Child A1 category.

Cracked injectorFinally we can get back to our original example. Here is just the recursive CTE in action, as you can see it correctly finds the root name for each category in the categories table. Finally, here is the full query of all products and their root category names. We now have a simple way to traverse arbitrarily deep hierarchical data very flexibly without introducing the overhead of keeping de-normalized data in a correct state.

The recursion is just another part of the normal SQL query, perfect for this use case. Services Process Work About Blog.This is a concept.

A recursive method calls itself. Recursive methods are used extensively in programming and in compilers. Recursion, notes. These algorithms help with complex problems. They solve problems and puzzles with brute force.

They exhaust all possibilities. Tip: Recursive algorithms are often used for complex searching and simulation. They add needless complication in other programs. Here is a recursive method. The method has 2 parameters, including a ref parameter. It checks a condition near the top of its method body, as many recursive algorithms do. Ref And: It calls itself again based on an incremented value of the parameter it receives.

The program also has a commented-out exception. Tip: This demonstrates the appearance of the method call stack frames in a recursive algorithm. End: The primitive example here continues until it sums up a value of 10 by incrementing an integer. Call stack: The call stack has six method stack frames with the Recursive method signature in them. WriteLine total ; Console. Exception thrown when throw uncommented: Unhandled Exception: System.

Exception: End at Program. Main in This may be the shortest valid C program that will crash. The Main method calls Main. The stack will overflow, leading to a memory error. StackOverflowException Tip: The exception here is a good thing, as it stops a process that would otherwise continue infinitely, wasting time and resources. Tail recursion.Procedures have a limited amount of space for variables.

Each time a procedure calls itself, more of that space is used. A procedure that calls itself is a recursive procedure. A recursive procedure that continuously calls itself eventually causes an error.

For example:. This error may be less obvious when two procedures call each other indefinitely, or when some condition that limits the recursion is never met. Recursion does have its uses. For example, the following procedure uses a recursive function to calculate factorials. You should test your recursive procedure to make sure it does not call itself so many times that you run out of memory. If you get an error, make sure your procedure is not calling itself indefinitely.

After that, try to conserve memory by:. Have questions or feedback about Office VBA or this documentation? Please see Office VBA support and feedback for guidance about the ways you can receive support and provide feedback. Skip to main content. Contents Exit focus mode. After that, try to conserve memory by: Eliminating unnecessary variables. Using data types other than Variant. Re-evaluating the logic of the procedure.

You can often substitute nested loops for recursion.

**Comparing Iterative and Recursive Factorial Functions**

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### Recursive Loop Example

Any additional feedback? Skip Submit. Is this page helpful?Recursion means "defining a problem in terms of itself".

This can be a very powerful tool in writing algorithms. Recursion comes directly from Mathematics, where there are many examples of expressions written in terms of themselves.

### Common examples of loops using recursion in Python

Recursion is the process of defining a problem or the solution to a problem in terms of a simpler version of itself. Here the solution to finding your way home is two steps three steps.

First, we don't go home if we are already home. Secondly, we do a very simple action that makes our situation simpler to solve. Finally, we redo the entire algorithm. The above example is called tail recursion. This is where the very last statement is calling the recursive algorithm.

Tail recursion can directly be translated into loops. Another example of recursion would be finding the maximum value in a list of numbers. The maximum value in a list is either the first number or the biggest of the remaining numbers. Here is how we would write the pseudocode of the algorithm:. The "work toward base case" is where we make the problem simpler e. The recursive call, is where we use the same algorithm to solve a simpler version of the problem.

The base case is the solution to the "simplest" possible problem For example, the base case in the problem 'find the largest number in a list' would be if the list had only one number Adding three numbers is equivalent to adding the first two numbers, and then adding these two numbers again.

Note, in Matlab, a function can be called without all the arguments. The nargin function tells the computer how many values were specified. This reduces the number of parameters nargin sent in to the function from 3 to 2, and 2 is the base case! In a recursive algorithm, the computer "remembers" every previous state of the problem. This information is "held" by the computer on the "activation stack" i. Consider a rectangle grid of rooms, where each room may or may not have doors on the North, South, East, and West sides.

How do you find your way out of a maze? Here is one possible "algorithm" for finding the answer:. The "trick" here is of course, how do we know if the door leads to a room that leads to the exit?

The answer is we don't but we can let the computer figure it out for us.How to begin Get the book.

Practice problems Quizzes. A useful way to think of recursive functions is to imagine them as a process being performed where one of the instructions is to "repeat the process". This makes it sound very similar to a loop because it repeats the same code, and in some ways it is similar to looping.

On the other hand, recursion makes it easier to express ideas in which the result of the recursive call is necessary to complete the task. Of course, it must be possible for the "process" to sometimes be completed without the recursive call. One simple example is the idea of building a wall that is ten feet high; if I want to build a ten foot high wall, then I will first build a 9 foot high wall, and then add an extra foot of bricks.

Conceptually, this is like saying the "build wall" function takes a height and if that height is greater than one, first calls itself to build a lower wall, and then adds one a foot of bricks.

The computer keeps function calls on a stack and once too many are called without ending, the program will crash. Why not write a program to see how many times the function is called before the program terminates?

Keep in mind, it is not a function restarting itself, it is hundreds of functions that are each unfinished with the last one calling a new recurse function.

It can be thought of like the Russian dolls that always have a smaller doll inside. Each doll calls another doll, and you can think of the size being a counter variable that is being decremented by one. Think of a really tiny doll, the size of a few atoms. You can't get any smaller than that, so there are no more dolls. Normally, a recursive function will have a variable that performs a similar action; one that controls when the function will finally exit.

The condition where the function will not call itself is termed the base case of the function. Basically, it is an if-statement that checks some variable for a condition such as a number being less than zero, or greater than some other number and if that condition is true, it will not allow the function to call itself again.

Or, it could check if a certain condition is true and only then allow the function to call itself. This is a good base case, but if it is not properly set up, it is possible to have an base case that is always true or always false. Once a function has called itself, it will be ready to go to the next line after the call. It can still perform operations. One function you could write could print out the numbers How can you use recursion to write a function to do this?

Simply have it keep incrementing a variable passed in, and then output the variable This is just the beginning of the usefulness of recursion.

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